Oct 22, 2014 01:01 AM
Matrix: Simulating the world Part I - Particle models
http://plus.maths.org/content/os/issue42...nell/index
EXCERPT: Building models forms the core of many areas of scientific and engineering research. Essentially, a model is a representation of a complex system that has been simplified in different ways to help understand its behaviour. An aeronautical engineer, for example, might build a miniaturised physical model of a fighter plane to test in a wind tunnel. In modern times, more and more modelling is being performed by computers — running mathematical models at very high rates of calculations. A computer model of the flow of air over a supersonic wing is incredibly sophisticated, but it is based on very basic principles of program design and simulation. In this article, the first half of a two-part feature on model behaviour, we'll take a look at how simple computer models can be programmed to study some very interesting natural systems as well as focus on how a few scientists are using similar models in their own front-line research....
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Matrix: Simulating the world Part II: cellular automata
http://plus.maths.org/content/matrix-sim...r-automata
EXCERPT: In the first part of Simulating the World we saw how simple mathematical models can be built to study everything from the flocking of birds to the collision of entire galaxies. In these examples, a matrix, or a grid of numbers, was used as a convenient way of storing information on all the objects included in the simulation, so that it can be updated each time step as the simulation progresses. In this second article, we'll take a look at another class of mathematical models; ones where the matrix or array isn't just a way of storing information during the simulation, but actually is the simulation itself.
Many real-world situations can be simplified as a sequence of objects in a line or an arrangement across a flat space — in other words, they can be faithfully represented by either a list of numbers (a one-dimensional matrix) or a regular grid of cells (a two-dimensional matrix). During the course of the simulation, the objects interact with those near-by according to a set of predefined rules, with the identity of each discrete position on the line or plane changing over time. Such a system is called a cellular automaton model....
http://plus.maths.org/content/os/issue42...nell/index
EXCERPT: Building models forms the core of many areas of scientific and engineering research. Essentially, a model is a representation of a complex system that has been simplified in different ways to help understand its behaviour. An aeronautical engineer, for example, might build a miniaturised physical model of a fighter plane to test in a wind tunnel. In modern times, more and more modelling is being performed by computers — running mathematical models at very high rates of calculations. A computer model of the flow of air over a supersonic wing is incredibly sophisticated, but it is based on very basic principles of program design and simulation. In this article, the first half of a two-part feature on model behaviour, we'll take a look at how simple computer models can be programmed to study some very interesting natural systems as well as focus on how a few scientists are using similar models in their own front-line research....
- - - - - -
Matrix: Simulating the world Part II: cellular automata
http://plus.maths.org/content/matrix-sim...r-automata
EXCERPT: In the first part of Simulating the World we saw how simple mathematical models can be built to study everything from the flocking of birds to the collision of entire galaxies. In these examples, a matrix, or a grid of numbers, was used as a convenient way of storing information on all the objects included in the simulation, so that it can be updated each time step as the simulation progresses. In this second article, we'll take a look at another class of mathematical models; ones where the matrix or array isn't just a way of storing information during the simulation, but actually is the simulation itself.
Many real-world situations can be simplified as a sequence of objects in a line or an arrangement across a flat space — in other words, they can be faithfully represented by either a list of numbers (a one-dimensional matrix) or a regular grid of cells (a two-dimensional matrix). During the course of the simulation, the objects interact with those near-by according to a set of predefined rules, with the identity of each discrete position on the line or plane changing over time. Such a system is called a cellular automaton model....